Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int a[1000010];
bool bin_search(int n1) {
  int i;
  for (i = 1; i <= sqrt(2 * n1) + 1; i++) {
    int lo = i, hi = sqrt(2 * n1) + 1, mid;
    while (lo <= hi) {
      mid = (lo + hi) >> 1;
      if (a[mid] == n1 - a[i])
        return true;
      else if (a[mid] < n1 - a[i])
        lo = mid + 1;
      else
        hi = mid - 1;
    }
  }
  return false;
}
int main() {
  int n1, i;
  cin >> n1;
  a[0] = 0;
  for (i = 1; i <= sqrt(2 * n1) + 1; i++) a[i] = a[i - 1] + i;
  if (bin_search(n1)) {
    cout << "YES"
         << "\n";
    return 0;
  }
  cout << "NO"
       << "\n";
  return 0;
}